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By using an inductive procedure we prove that the Galerkin finite element approximations of electromagnetic eigenproblems modelling cavity resonators by elements of any fixed order of either Nedelec’s edge element family on tetrahedral meshes are convergent and free of spurious solutions. This result is not new but is proved under weaker hypotheses, which are fulfilled in most of engineering applications. The method of the proof is new, instead, and shows how families of spurious-free elements can be systematically constructed. The tools here developed are used to define a new family of spurious-free edge elements which, in some sense, are complementary to those defined in 1986 by Nedelec.

@article{Caorsi2001, abstract = {By using an inductive procedure we prove that the Galerkin finite element approximations of electromagnetic eigenproblems modelling cavity resonators by elements of any fixed order of either Nedelec’s edge element family on tetrahedral meshes are convergent and free of spurious solutions. This result is not new but is proved under weaker hypotheses, which are fulfilled in most of engineering applications. The method of the proof is new, instead, and shows how families of spurious-free elements can be systematically constructed. The tools here developed are used to define a new family of spurious-free edge elements which, in some sense, are complementary to those defined in 1986 by Nedelec.}, author = {Caorsi, Salvatore, Fernandes, Paolo, Raffetto, Mirco}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique}, keywords = {electromagnetic eigenproblems; new families of edge elements; Galerkin finite element approximations; convergence; spurious modes; discontinuous material properties; symmetry exploitation; mixed boundary conditions; discrete compactness}, language = {eng}, number = {2}, pages = {331-354}, publisher = {EDP-Sciences}, title = {Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements}, url = {http://eudml.org/doc/194053}, volume = {35}, year = {2001},}

TY - JOURAU - Caorsi, SalvatoreAU - Fernandes, PaoloAU - Raffetto, MircoTI - Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elementsJO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse NumériquePY - 2001PB - EDP-SciencesVL - 35IS - 2SP - 331EP - 354AB - By using an inductive procedure we prove that the Galerkin finite element approximations of electromagnetic eigenproblems modelling cavity resonators by elements of any fixed order of either Nedelec’s edge element family on tetrahedral meshes are convergent and free of spurious solutions. This result is not new but is proved under weaker hypotheses, which are fulfilled in most of engineering applications. The method of the proof is new, instead, and shows how families of spurious-free elements can be systematically constructed. The tools here developed are used to define a new family of spurious-free edge elements which, in some sense, are complementary to those defined in 1986 by Nedelec.LA - engKW - electromagnetic eigenproblems; new families of edge elements; Galerkin finite element approximations; convergence; spurious modes; discontinuous material properties; symmetry exploitation; mixed boundary conditions; discrete compactnessUR - http://eudml.org/doc/194053ER -